{
  "abstract": "We study the semidefinite programs (SDPs) of quantum information whose variables are density operators, measurement operators, or unbounded positive semidefinite operators, together with their thermodynamic regularizations by the von Neumann, Fermi-Dirac, and Bose-Einstein entropies, which have been associated with Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, respectively. We find that this correspondence is exact: the Fermi-Dirac and Bose-Einstein regularized SDPs coincide with the constrained free-energy minimization of an ideal Fermi or Bose gas whose Hamiltonian and non-commuting charges are the second quantizations of the SDP data and whose one-body density matrix is the SDP variable, while the Boltzmann framework corresponds to the single-particle case. We show that the three frameworks can be unified under one framework, in which each entropy-regularized dual is, up to a term linear in the chemical potentials, the grand potential of the corresponding system; the duals are unconstrained and concave in the chemical-potential vector, with gradient and Hessian given by thermal expectation values that hybrid quantum-classical algorithms can estimate. We further identify the Fermi-Dirac and Bose-Einstein relative entropies with the Umegaki relative entropy between quasi-free states, which yields their monotonicity under gauge-covariant Gaussian channels. The result places a wide class of SDPs and their solvers within the thermodynamics of ideal quantum gases and points to extensions to interacting gases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.21123",
  "author_total": 4,
  "authors": [
    {
      "name": "Michele Minervini"
    },
    {
      "name": "Nana Liu"
    },
    {
      "name": "Dhrumil Patel"
    },
    {
      "name": "Mark M. Wilde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vd282nx5pshz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.21123",
  "fulltext_url": null,
  "id": "7vd282nx5pshz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.21123",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204109830",
  "pdf_url": "https://arxiv.org/pdf/2608.21123",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vd282nx5pshz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2608.21123",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.21123"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Semidefinite optimization as many-body thermodynamics: Boltzmann, Fermi-Dirac, and Bose-Einstein frameworks",
  "title_text": "Semidefinite optimization as many-body thermodynamics: Boltzmann, Fermi-Dirac, and Bose-Einstein frameworks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/7vd282nx5pshz",
  "venue": "arXiv",
  "versions": []
}